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The current article focuses on the examination of nonlinear instability and dynamic transitions in a double-diffusive rotating couple-stress fluid layer. The analysis was based on the newly developed dynamic transition theory by T. Ma and S. Wang. Through a comprehensive linear spectrum analysis and investigation of the principle of exchange of stability (PES) as the thermal Rayleigh number crosses a threshold, the nonlinear orbital changes during the transition were rigorously elucidated utilizing reduction methods. For both single real and complex eigenvalue crossings, local pitch-fork and Hopf bifurcations were discovered, and directions of these bifurcations were identified along with transition types. Furthermore, nondimensional transition numbers that signify crucial factors during the transition were calculated and the orbital structures were illustrated. Numerical studies were performed to validate the theoretical results, revealing the relations between key parameters in the system and the types of transition. The findings indicated that the presence of couple stress and a slow diffusion rate of solvent and temperature led to smoother nonlinear transitions during convection. [ABSTRACT FROM AUTHOR]

The analysis of entropy generation provides valuable information for the design and optimization of thermal systems. Solar stills are used for water desalination and purification. Using renewable energies, they provide a sustainable solution for drinking water supply in remote areas and off-grid situations. This work focuses on the 3D numerical study of entropy generation in a two-stage solar still subjected to the natural double diffusion convection phenomenon in the presence of CNT nanoparticles. The effects of Rayleigh number, buoyancy ratio, and nanofluid concentration on thermal, solutal, and viscous irreversibilities and flow structure were studied. The results show that increasing the buoyancy ratio leads to an increase in thermal and solutal entropy generation. The results of this study also show that total entropy is minimal for positive volume force ratios, N, at a nanoparticle volume fraction of around 3%, and for negative N ratios, at a volume fraction of around 4%. [ABSTRACT FROM AUTHOR]

The influence of the throughflow and gravity fluctuation on thermosolutal convection in an anisotropic porous bed with the Darcy–Brinkman effect is considered numerically. The critical Rayleigh numbers for the onset of stationary and oscillatory modes have been found via linear instability analysis. The impact of various gravitational functions in the presence of throughflow on stability is studied. The analysis has been carried out for decreasing and increasing gravity fluctuations. The convective problem has been numerically analyzed using a single-term Galerkin approach. The results show that the mechanical anisotropy parameter and Lewis number have a destabilizing effect, while the thermal anisotropy parameter, Darcy number, solutal Rayleigh number, throughflow parameter, and gravity parameter have a stabilizing effect on stationary and oscillatory convection. It is clear that the system changes in a way that makes it more stable for case (iii) gravity fluctuation and more unstable for case (iv) gravity fluctuation. [ABSTRACT FROM AUTHOR]

The present work has mathematically modeled the peristaltic flow in nanofluid by using thermal radiation, induced a magnetic field, double-diffusive convection, and slip boundary conditions in an asymmetric channel. Peristalsis propagates the flow in an asymmetric channel. Using the linear mathematical link, the rheological equations are translated from fixed to wave frames. Next, the rheological equations are converted to nondimensional forms with the help of dimensionless variables. Further, the flow evaluation is determined under two scientific assumptions: a finite Reynolds number and a long wavelength. Mathematica software is used to solve the numerical value of rheological equations. Lastly, the impact of prominent hydromechanical parameters on trapping, velocity, concentration, magnetic force function, nanoparticle volume fraction, temperature, pressure gradient, and pressure rise are evaluated graphically. [ABSTRACT FROM AUTHOR]

This work employs single-mode equations to study convection and double-diffusive convection in a porous medium where the Darcy law provides large-scale damping. We first consider thermal convection with salinity as a passive scalar. The single-mode solutions resembling steady convection rolls reproduce the qualitative behavior of root-mean-square and mean temperature profiles of time-dependent states at high Rayleigh numbers from direct numerical simulations (DNS). We also show that the single-mode solutions are consistent with the heat-exchanger model that describes well the mean temperature gradient in the interior. The Nusselt number predicted from the single-mode solutions exhibits a scaling law with Rayleigh number close to that followed by exact 2D steady convection rolls, although large aspect ratio DNS results indicate a faster increase. However, the single-mode solutions at a high wavenumber predict Nusselt numbers close to the DNS results in narrow domains. We also employ the single-mode equations to analyze the influence of active salinity, introducing a salinity contribution to the buoyancy, but with a smaller diffusivity than the temperature. The single-mode solutions are able to capture the stabilizing effect of an imposed salinity gradient and describe the standing and traveling wave behaviors observed in DNS. The Sherwood numbers obtained from single-mode solutions show a scaling law with the Lewis number that is close to the DNS computations with passive or active salinity. This work demonstrates that single-mode solutions can be successfully applied to this system whenever periodic or no-flux boundary conditions apply in the horizontal. [ABSTRACT FROM AUTHOR]

A three-dimensional computational study of double-diffusive natural convection was conducted to explore the impact of tilt on the thermal and solutal performance of a floating pyramidal solar still filled with an air-steam mixture. In the present work, the still is cooled from the upper walls and is maintained at a low vapor concentration. The bottom wall of the still is maintained at a hot temperature and high concentration. Four different models of baffles placed in the upper region of the solar still have been studied. The mathematical formulation of the equations governing the problem is based on the vector current potential -vorticity formalism. The numerical method of finite volumes is used. The effect of Rayleigh and tilt angle of the floating solar still on the flow structure, iso-temperatures, iso-concentrations, and heat and mass transfer rates were examined. The most relevant results of this study are (i) an uncooled air-vapor mixture outlet was observed during tilting for the solar still equipped with a small, flat baffle, (ii) triangular and curvilinear baffle configurations are suitable to guide the air-vapor mixture towards the cold walls during the tilting of the solar still floating on the sea, and (iii) the triangular baffle configuration is the most relevant design, enhancing thermal and solutal performance by 20%. [ABSTRACT FROM AUTHOR]

A theoretical study is presented to examine entropy generation in double-diffusive convection in an Electro-osmotic flow (EOF) of nanofluids via a peristaltic microchannel. Buoyancy effects due to change in temperature, solute concentration and nanoparticle volume fraction are also considered. This study was performed under lubrication and Debye-Hückel linearization approximation. The governing equations are solved exactly. The effect of dominant hydrodynamic parameters (thermophoresis, Brownian motion, Soret and Dufour), Grashof numbers (thermal, concentration and nanoparticle) and electro-osmotic parameters on double-diffusive convective flow are discussed. Moreover, trapping, pumping, entropy generation number, Bejan number and heat transfer rate were also examined under the influence of pertinent parameters such as the thermophoresis parameter, the Brownian motion parameter, the Soret parameter, the Dufour parameter, the thermal Grashof number, the solutal Grashof number, the nanoparticle Grashof number, the electro-osmotic parameter and Helmholtz–Smoluchowski velocity. The electro-osmotic parameter powerfully affected the velocity profile. The magnitude of total entropy generation increased as the thermophoresis parameter and Brownian motion parameter increased. Soret and the Dufour parameter had a strong tendency to control the temperature profile and Bejan number. The findings of the present analysis can be used in clinical purposes such as cell therapy, drug delivery systems, pharmaco-dynamic pumps and particles filtration. [ABSTRACT FROM AUTHOR]